In the right-hand isosceles triangle, the two bottom angles are equal.
The three angles add up to 180°, so:
\(50+2(2y+64)=180\)
⇒\(50+4y+128=180\)
⇒\(4y+178=180\)
⇒\(4y=2\)
⇒\(y=\frac{1}{2}\)
The angle \(2y+64\) comes out as \(2(\frac{1}{2})+64=1+64=65\)
The angle to the side of it is 180-65=125.
In the left-hand triangle, the angle at the left and the angle at the top are equal.
In this triangle:
\(125+2(45-\frac{x}{4})=180\)
⇒\(125+90-\frac{x}{2}=180\)
⇒\(215-\frac{x}{2}=180\)
⇒\(215-180=\frac{x}{2}\)
⇒\(\frac{x}{2}=35\)
⇒\(x=70\)
So \(x=70\) and \(y=\frac{1}{2}\)
